Modern physics defines fundamental forces and particles as particular “fields”. I have read some things like “gauge symmetry” play an important role in these theories.

I have looked up a good reference material on axiomatic quantum field theory, which has sections on the ontological interpretations of AQFTs, but I’d like a gentler introduction first.

I think there are two questions. Mathematically, do contemporary physicists prefer a certain level of expressive power of a formal system, in order to formulate and express the constructs of mathematical physics?

Ontologically, can axiomatic physical theories admit easy interpretations as to what inherent phenomenological categories they take as primary? Which ones? For example, perhaps a certain AQFT can ‘construct time’ out of something else, but it requires the existence of some category, like energy, about which all the derivations of the theory are intepreted as true statements about the nature of that something called ‘energy’.

  • You are looking for The Character of Physical Law by Richard Feynman, 1965.
    – g s
    Commented Apr 27 at 19:25
  • Axiomatic theories are generally malleable, and axiomatic physical theories especially so, they can be easily reformulated into mathematically equivalent ones with different primitives and hence different "ontological bases". Special relativity, for example, is mathematically equivalent to Lorentz's aether, quantum field theories based on fields to those based on particles, and it is even more pronounced in string theory that admits multiple completely different ontologies due to its non-trivial dualities, see Dawid.
    – Conifold
    Commented Apr 27 at 20:06
  • Of interest: Aristotelian metaphysics, Neoplatonic thought, Maimonides
    – Rabbi Kaii
    Commented Apr 27 at 23:54

2 Answers 2


QFTs are reducing particles to algebraic structures which are in fact mathematical abstractions. The ontology of reality IS identified with these mathematical constructs. It's not that mathematics are used in order to describe the ontological interractions, it's that these mathematical structures have become the ontology themselves.

When physicists see inside nature, they see things that although are able to model as mathematical constructs, they are unable to describe them by language in a meaningful (common sense) way. So these mathematical representations of the way reality appears to us has already become the new ontology.

For example, the state is a potentiality (undecided position) and the probability is the possibility of specific position when an observation is to be made; but position of what? of a particle? which is now a field? or for compatibility reasons a continuesly created and destroyed thing? : thus a mathematical construct!


A really useful answer to this question would come from a physics practitioner who has completed a graduate program in mathematical physics. I will provide a slightly useful answer instead.

The basis of modern physics is the idea that everything has a cause (i.e., magic and miracles don't operate in the physical world) and the most unambiguous way of expressing causal relationships is by use of the language of mathematics. That language lets us predict behavior and calculate answers. Comparing these to experimental measurements lets us gauge the correctness of those causal models.

In assembling those models, physicists begin with certain bedrock principles known to be valid in the universe we inhabit. Among these are conservation laws or "bookkeeping rules" (there's no free lunch, anything borrowed must be paid back, whatever you take has to be paid for) and other more derivative principles like frequency and energy can't be negative, probabilities of outcomes must sum to one and so forth.

The process of creating causal models from scratch is such that for any new model to hope to be a correct description of reality, it must obey those bedrock principles- otherwise the universe that model describes is not the one we inhabit.

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .